The important distinction: “You cannot stop me from responding” does not mean “You must debate me”

This is probably the most important qualification to my argument.

Suppose A makes a public claim and B replies with a rebuttal.

A says:

“Don't bother responding to me.”

A is certainly entitled to decline to continue the discussion.

But that does not logically mean:

“Therefore B should not respond.”

B can respond for the benefit of the wider audience rather than for A.

This is especially important on social media.

The exchange is not necessarily:

A and B

It can be:

A and public audience

and then:

B and public audience

So B's response does not have to be understood as an attempt to persuade A.

B might be saying:

“I don't expect the original author to change his mind. I'm responding because other people reading this post may otherwise accept the claim.”

That is a perfectly coherent reason for responding.